Mechanical Devices for Snail-Like Locomotion

Mechanical Devices for Snail-Like Locomotion

Brian Chan, Susan Ji, Katherine Koveal, Anette Hosoi

Hatsopolous Microfluids Laboratory

Department of Mechanical Engineering

Massachusetts Institute of Technology

Abstract

In order to better understand the propulsion mechanisms of live gastropods, we have constructed two mechanical snails, Robosnail 1 and Robosnail 2. Each uses a different mechanical strategy to move on a thin layer of viscous fluid. Robosnail 1 uses a flexible flapping sheet to generate lubrication pressures in a viscous Newtonian fluid which in turn propel the snail. Robosnail 2 uses a compressible sliding sheet on a layer of Laponite, a non-Newtonian, finite-yield stress fluid with characteristics similar to those of snail mucus.

Introduction

Figure 1: Underside of Leopard slug Limax maximus during locomotion showing wave and interwave segments. Here, waves propagate in the direction of locomotion.

Gastropods such as snails and slugs (with the exception of free-swimming species) move over solid surfaces lubricated by a thin layer of mucus. It has been noted that when snails move, they generate a train of moving waves along the foot (see figure 1). Depending on the type of snail, the waves may be compression waves moving from the tail to the head (direct waves) or expansion waves from the head to the tail (retrograde waves) [10-12]. Close observation shows that the foot is affixed by mucus to the substrate in the area between waves (the interwave) and moves within the wave. This mode of locomotion has been termed adhesive locomotion by Denny [5-7]. It is commonly observed that most land snails used direct waves, while most aquatic snails use retrograde waves. This correlation between habitat and locomotion method leads us to believe that terrestrial species may have evolvedan alternate mechanism of motion.

Robosnail 1

Robosnail 1 was built to explore the possibility that marine snails and other aquatic creatures such as flatworms use backwards waving deformations of the body to generate thrust forces in the thin layer of fluid. As the foot of the snail waves over a thin layer of viscous Newtonian fluid, it generates a high pressure near the ground where the fluid is being squeezed and a low pressure where the fluid is being pulled apart. The pressure forces acting on the sloped areas of the sinusoidal foot act to propel the snail. This means of locomotion bears considerable similarity to peristaltic pumping of fluids through flexible channels [2,4,8]. The primary difference is that the force applied by the boundary and transmitted through the fluid to the substrate is used to move both the boundary and the fluid, rather than being used to pump the fluid alone.

Figure 2: Exploded view of Robosnail 1

Robosnail 1 has a solid polycarbonate body (see figure 2) with a total weight is 1.67 N. Its foot is powered by an external DC power source, capable of supplying 1.5, 3.0 and 4.5 volts. The motor is connected to a variable-speed gear box. A toothed pulley connects the gearbox to a shallow brass helix which passes through an array of aluminum sheets perforated with slots. Each of the sheets is constrained to vertical motion as they ride in equally spaced slots along the body. The bottom edges of the sheets are directly glued onto a flexible foam sheet. When the helix is spun by the motor and gearbox, it causes the plates to translate up and down inside their tracks in a moving sinusoidal wave (evident when viewed from the side). The wave is transferred directly to the foam sheet. This sinusoidal wave generates regions of high pressure in front of the wave where the fluid is squeezed into a narrow gap, and regions of low pressure behind the wave where the fluid is allowed to expand. These pressures generate forces normal to the interface, driving the snail in the opposite direction of the wave (reminiscent of the retrograde waves observed in marine snails).

To test the efficacy of this mechanism, a track slightly larger than the width of the snail, to minimize the leakage of fluid past the open sides of the foot, was constructed. A laser, fitted with a lens to emit a plane of light, was fixed at an angle of 45 degrees with respect to the bottom of the clear channel. The line of the laser hitting the foam sole, seen from the underside, reflects the height of the wave relative to the bottom of the channel, and the profile of the film thickness becomes clearly visible from an underside view. The track was filled with 0.5 mm thick layer of glycerol and the Robosnail was activated on top of the layer. After the motion reached steady state, measurements of wave speed, foot height (revealed by the laser), and snail speed were recorded.Robosnail 1 was tested using varying wavespeeds and as expected, the direction of motion was found to be opposite the direction of wave propagation.

Performing a two-dimensional lubrication analysis on the thin film of Newtonian fluid, we predict that the velocity of the snail scales linearly with wave speed:

where vs is the velocity of the snail, vw is the velocity of the wave, h0 is the average height of the fluid layer, and a is the amplitude of the waving foot. The correct scaling for the snail velocity was observed experimentally (figure 3) however, the coefficient was considerably smaller than the value predicted by the analytical solution. The model predicts a lower coefficient as gap thickness increases; however, the data corresponded to a larger gap (a/h0 = 0.5) than was measured in the experiment (a/h0≈ 1). This discrepancy is most likely due to leakage of fluid from the side of the finite-width robot, which reduces the effectiveness of the propulsion mechanism.

Figure 3: (Left) Analytical solution for an infinite waving sheet, and (Right) experimental results. The best fit of the linear coefficient in the experimental data corresponded to a value of a/h0 = 0.5.

Robosnail 2

Robosnail 2 was built to mimic the direct wave motion of land snails. The bottom interwave area of a snail’s foot is adhered to the substrate via the fluid layer while a traveling wave of compression causes a small net translation as it propagates from one end of the foot to the other.

Unlike real snails, the foot of Robosnail 2 is made of five discrete, sliding sections, while live snails have a continuous foot of muscle. Each of the five foot sections of Robosnail 2 move forward a small fixed amount in relation to the body, after which they all return to their original positions. These small motions occur in sequence as illustrated in figure 4. Rheological properties of the interstitial fluid play a key role in the propulsion mechanism of Robosnail 2. As each wave propagates forward, the interwave areas must adhere to the substrate to prevent the snail from slipping backwards. Conversely, the moving portion of the foot must be allowed to slide freely forwards. This is only possible if the interstitial fluid possesses a finite yield stress. In the interwave regions, the fluid is unstressed and acts as a solid gluing the foot to the substrate; in the wave regions, the snail must provide sufficient stress to induce the non-Newtonian fluid to yield providing a lubricating layer for the wave.

Figure 4: Action sequence of Robosnail 2 foot segments. Black segments represent interwave or stationary areas; grey segments indicate wave areas of propagation. In the final frame, the body shifts forward relieving the tension in the leaf springs.

Figure 5: Comparison of stress-strain rate characteristics of snail mucus and Laponite.

Instead of mucus as a lubricating layer, Laponite was used, chosen for its pronounced shear thinning effects [1,13], finite yield stress and availability. Though the mechanical properties of Laponite and snail mucus are quantitatively different, both exhibit the similar non-Newtonian properties that allow for adhesive locomotion.

In order for the snail to propel itself forward, the force provided by the viscous shear of the moving segment must balance (or be exceeded by) the force sustained by the stationary foot segments. When the speed of the moving foot section is small such that the viscous stress is much less than the yield stress, one can approximate the stress underneath the shearing Laponite by the yield stress value of about 100 Pa (see figure 5), and the force on the moving part of the foot to be the product of the area of the moving section and the yield stress, allowing us to determine the actuation force.

Figure 6: Exploded view of Robosnail 2

Robosnail 2 was designed to mimic the vertical wallclimbing ability of adhesive locomotion using a finite yield-stress fluid. For wall-climbing to be possible, the force per unit area of stationary foot area must be less than the yield stress of Laponite. In vertical wall-climbing, this force is dominated by the weight of the snail. Since the yield stress of Laponite is only about 100 Pa, Robosnail 2 needed to be as light as possible. To save weight, Robosnail 2 is actuated using five 10 cm lengths of Nitinol shape-memory alloy wire [9] rather than electric motors. The finished prototype weighed 0.31 N.
The five Nitinol wires are attached to nylon cords wrapped 180 degrees around a pulley and tied to five sheets of polycarbonate (see figure 6). Each of the sheets is attached to a pair of guides that allow only fore-aft translation. A leaf spring held by the main body returns each of the sheets to its original position when there is no other force. The springs apply the restoring forces necessary to return the wires to their outstretched positions.
The wires are crimped in loops at the ends, one end is tied to the cords controlling the foot, and the other end of each wire is looped around adjustable brass fasteners to allow proper tightening of the wire and cords. It was important for the wires to be correctly tensioned such that the springs succeed in re-stretching the wires, but not so tight as to limit the motion of the muscle wires. The tightness adjustment is achieved by turning the screws through which the wire mounts are threaded.

To test the wall climbing ability of Robosnail 2, we mounted it on a tiltable platform covered in a 1.5 mm thick layer of Laponite. The bulk of the Laponite was observed to keep its shape as a fixed layer on the platform as the robot slid along. This observation suggests that only a small layer of the Laponite touching the foot segment yielded into liquid form, while the rest remained solid. Robosnail 2 was able to climb the Laponite-coated surface tilted at any angle, including both a vertical and fully inverted position (see figure 7).

Figures 7: Testing the inverted locomotion capability of Robosnail 2 and displacement per cycle graph of Robosnail 2.

The experiment showed that the motion per cycle is in all cases slightly less than the translation of one foot. Ideally the slip velocity should be zero and the snail displacement per cycledshould be ΔL (this would be along the line d/ΔL = 1). The slipping effect of the stationary sections can be explained by several phenomena: neither the Laponite layer nor the foam rubber of Robosnail foot sections was perfectly flat, therefore if the moving section hits a lump or other imperfection in the Laponite, the local stress would exceed the yield stress. Another cause for slippage is the Laponite under the stationary sections may have not had enough time to re-solidify. This last problem could possibly be remedied by increasing the time of each cycle, to allow the Laponite to re-solidify at the expense of slowing down the translational speed of the snail. Finally, it was observed that there was de-lamination of the Laponite layer from the segments of the foot, decreasing the traction of the stationary foot segments. The most slip occurs between 60 and about 120 degrees, when the high angle of tilt decreased the normal force of the robot’s weight and thus the traction. At high tilt, much of the adhesive force of the Laponite support both the weight of the snail and the viscous resistance of the moving foot section, while at near-flat angles near 0 and 180, the adhesive force mostly resists just the friction on the moving foot. We should expect a minimum displacement somewhere between 90 degrees and 180 degrees, where gravity works to decrease traction and to increase the resistive force of the weight; this is indeed supported by the data. Though there was some slipping at all angles of incline, Robosnail 2 was able to consistently propel itself forward at all inclined angles.

Conclusions

The results of these experiments confirm the feasibility of snail-like motion for small machines, and introduce a new type of application for unconventional actuators for robots and related machines. Although the actual speeds of the devices did not reach the values predicted by theory, the fundamental concept is proven by the motion of the devices. Furthermore, there is room for more work in improving efficiency and optimization of both mechanisms.

References

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